Problem: Which of the following numbers is a multiple of 14? ${69,70,75,80,85}$
Solution: The multiples of $14$ are $14$ $28$ $42$ $56$ ..... In general, any number that leaves no remainder when divided by $14$ is considered a multiple of $14$ We can start by dividing each of our answer choices by $14$ $69 \div 14 = 4\text{ R }13$ $70 \div 14 = 5$ $75 \div 14 = 5\text{ R }5$ $80 \div 14 = 5\text{ R }10$ $85 \div 14 = 6\text{ R }1$ The only answer choice that leaves no remainder after the division is $70$ $ 5$ $14$ $70$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $70$ $70 = 2\times5\times7 14 = 2\times7$ Therefore the only multiple of $14$ out of our choices is $70$. We can say that $70$ is divisible by $14$.